OK, I'm starting to think that the team may get prorated cap credits if Byrd did retire. It's tough to find specifics on retired players + cap credits. But retirement is listed under types of a "Forfeitable Breach" in the CBA, and there are other cases of teams getting cap credits after forfeitable breaches. Unfortunately, those credits may not come until after a Brees retirement:

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While conducting research for this blog post, I looked at a couple of cases to see how long it took a team to get a cap credit for recouped money. The Patriots released Jonathan Fanene on August 21, 2012 with a “failure to disclose physical condition” designation. The Patriots filed a grievance seeking some, if not all, of the $3.85 million signing bonus Fanene received when he signed with the team March 20. The grievance hearing was held in July of 2013. On September 21, 2013 ESPNBoston.Com’s Mike Reiss reported that “The Patriots and defensive lineman Jonathan Fanene (represented by the NFL Players Association) settled their grievance within the past week, according to sources, and part of the settlement is that the Patriots won’t have to pay Fanene the final $1.35 million of his $3.85 million signing bonus… We can now officially close the book on the Patriots’ failed Fanene signing, with Fanene able to keep $2.5 million of the original signing bonus and the Patriots receiving a credit on their 2013 salary cap.” On March 13, 2014 update OvertheCap’s owner, Jason Fitzgerald, tweeted referring to the Patriots 2014 adjusted cap number that “the official number (also includes the 504k adjust and 360k of fanene is a direct credit and not in adjustment”. To sum up it took the Patriots two years to get a credit for a grievance filed in 2012. It took the Falcons five years to get a $3 million credit for Michael Vick. In August 2007 they won a grievance against Vick for around $20 million. - See more at: LINK